Problem : If $ax^4 +bx^3+cx^2+dx+e= $ $$
\begin{vmatrix}
x^3+3x & x-1 & x+3 \\
x+1 & -2x & x-4 \\
x-3 & x+4 & 3x \\
\end{vmatrix}
$$
Then find $e$.
Solution:
I know to solve the question by expanding the determinant
But I want to find determinant by using properties of determinant.
Please help
Best Answer
Considering @Arthur's leading comment, if we accept that this equation is being held for every value of $x$, so put for example $x=0$ to find out $e=0$. Note that we can see that for some $x$ the matrix is skew-symmetric matrix.